📚 Cambridge Economics Formula & Theorem Quick Reference | 剑桥经济公式定理速查手册
This quick reference handbook compiles essential formulas and theorems for Year 11 Cambridge Economics (IGCSE / O Level). Mastering these quantitative tools and key economic concepts will sharpen your exam technique and strengthen your understanding of how markets and economies work.
本速查手册汇编了 Year 11 剑桥经济学（IGCSE / O Level）的核心公式与定理。掌握这些定量工具和关键经济概念，能够提升你的应试技巧，并加深你对市场与经济运行方式的理解。
1. Price Elasticity of Demand (PED) | 需求价格弹性
PED measures the responsiveness of quantity demanded to a change in the good's own price. The basic formula uses percentage changes to give a coefficient that is normally negative, but economists often look at its absolute value.
需求价格弹性衡量需求量对商品自身价格变动的反应程度。基本公式使用百分比变化，得出的系数通常为负值，但经济学家通常关注其绝对值。
PED = %ΔQd ÷ %ΔP
Where %Δ = (New value − Original value) ÷ Original value × 100. If |PED| > 1, demand is price elastic; if |PED| < 1, demand is price inelastic; if |PED| rve is horizontal (PED = ∞), and a perfectly inelastic demand curve is vertical (PED = 0).
其中 %Δ =（新值 − 原值）÷ 原值 × 100。若 |PED| > 1，需求富有价格弹性；若 |PED| < 1，需求缺乏价格弹性；若 |PED| = 1，需求具有单位弹性。完全弹性需求曲线呈水平状（PED = ∞），完全无弹性需求曲线呈垂直状（PED = 0）。
2. Price Elasticity of Supply (PES) | 供给价格弹性
PES captures how responsive quantity supplied is to a change in price. Unlike PED, the sign is normally positive because a higher price encourages firms to produce more.
供给价格弹性反映供给量对价格变动的反应程度。与需求价格弹性不同，其值通常为正，因为价格上升会激励企业增加产量。
PES = %ΔQs ÷ %ΔP
When PES > 1, supply is price elastic; when PES < 1, supply is price inelastic. Factors such as production time, spare capacity, and the ease of storing inventory affect PES.
当 PES > 1 时，供给富有价格弹性；当 PES < 1 时，供给缺乏价格弹性。生产周期、闲置产能以及存货储存的难易程度等因素都会影响供给价格弹性。
3. Income Elasticity of Demand (YED) | 需求收入弹性
YED indicates how quantity demanded changes in response to a change in consumers' income. It helps classify goods as normal, luxury, or inferior.
需求收入弹性表明需求量如何随消费者收入的变化而变化。它有助于将商品划分为正常品、奢侈品或低档品。
YED = %ΔQd ÷ %ΔY
If YED > 0, the good is a normal good (positive relationship). For normal goods, YED > 1 suggests a luxury, while 0 < YED < 1 indicates a necessity. If YED < 0, the good is an inferior good.
若 YED > 0，该商品为正常品（正向关系）。对正常品而言，YED > 1 意味着其为奢侈品，0 < YED < 1 则为必需品。若 YED < 0，该商品为低档品。
4. Cross Elasticity of Demand (XED) | 需求交叉弹性
XED measures the responsiveness of demand for one good (A) when the price of another good (B) changes. Its sign reveals the relationship between the two goods.
需求交叉弹性衡量一种商品（A）的需求量对另一种商品（B）价格变动的反应程度。其正负号可揭示两种商品之间的关系。
XED = %ΔQd of good A ÷ %ΔP of good B
If XED > 0, the two goods are substitutes (e.g., tea and coffee). If XED < 0, they are complements (e.g., printers and ink cartridges). A value close to zero suggests the goods are unrelated.
若 XED > 0，两种商品互为替代品（如茶与咖啡）。若 XED < 0，它们互为互补品（如打印机与墨盒）。XED 值接近零表示两种商品不相关。
5. Total Revenue, Average Revenue and Profit | 总收益、平均收益与利润
Total revenue is the income a firm receives from sales. Average revenue is revenue per unit sold, and in most market structures it equals the price. Profit is what remains after subtracting total costs.
总收益是企业从销售中获得的收入。平均收益是每单位销售带来的收入，在多数市场结构中等于价格。利润是减去总成本后的剩余部分。
TR = P × Q
AR = TR ÷ Q = P
Profit = TR − TC
When a firm can set a single price, its demand curve is also its AR curve. Marginal revenue (MR) is the extra revenue from selling one more unit; for a straight-line demand curve, MR falls twice as steeply as AR.
当企业能制定单一价格时，其需求曲线也是平均收益曲线。边际收益（MR）是多售出一单位产品所带来的额外收入；对于线性需求曲线，边际收益曲线的斜率是平均收益曲线的两倍。
6. Costs of Production: Total, Average and Marginal Cost | 生产成本：总成本、平均成本与边际成本
Firms face fixed costs that do not vary with output and variable costs that change with production. Understanding how these costs behave is essential for profit calculations.
企业面临不随产量变动的固定成本以及随产量变化的可变成本。理解这些成本的习性对利润计算至关重要。
TC = TFC + TVC
AFC = TFC ÷ Q
AVC = TVC ÷ Q
ATC = TC ÷ Q = AFC + AVC
MC = ΔTC ÷ ΔQ
The MC curve cuts both the AVC and ATC curves at their minimum points. In the short run, at least one factor is fixed, so the law of diminishing returns causes MC to eventually rise.
边际成本曲线穿过平均可变成本和平均总成本曲线的最低点。在短期内，至少有一种要素固定，因此边际报酬递减规律导致边际成本最终上升。
7. Profit Maximisation Rule | 利润最大化法则
The fundamental decision rule for any firm is to produce at the output level where marginal cost equals marginal revenue, as long as price covers average variable cost in the short run.
任何企业的基本决策法则是在边际成本等于边际收益的产量水平上生产，只要短期内价格能覆盖平均可变成本。
Profit-maximising output: MC = MR
If MR > MC, the extra unit adds more to revenue than to cost, so the firm should expand output. If MR < MC, the extra unit costs more than it brings in, so the firm should reduce output.
若 MR > MC，新增单位的收益大于成本，企业应扩大产量。若 MR < MC，新增单位的成本大于收益，企业应减少产量。
8. Break-even Analysis | 盈亏平衡分析
Break-even occurs when total revenue equals total cost, so the firm makes neither a profit nor a loss. The break-even point can be calculated using contribution per unit.
盈亏平衡点出现在总收益等于总成本时，此时企业既不盈利也不亏损。盈亏平衡点可利用单位贡献毛利计算。
Break-even output = TFC ÷ (Price − AVC)
Here (Price − AVC) is the contribution per unit. The break-even chart plots TR and TC against output; their intersection marks the break-even point. Knowing this output helps firms set targets and evaluate risk.
这里的（价格 − 平均可变成本）即单位贡献毛利。盈亏平衡图将总收益和总成本相对于产量绘制出来，二者相交处即为盈亏平衡点。了解该产量有助于企业设定目标并评估风险。
9. Gross Domestic Product (GDP) | 国内生产总值
GDP measures the total value of all final goods and services produced within a country's borders in a given time period. The expenditure approach adds up spending by different sectors.
国内生产总值衡量在一定时期内一国境内生产的所有最终商品与服务的总价值。支出法将各经济部门的支出加总。
GDP = C + I + G + (X − M)
C stands for household consumption, I for business investment, G for government spending, X for exports, and M for imports. The income approach sums all factor incomes (wages, rent, interest, profit), while the output approach sums value added across industries.
C 表示家庭消费，I 为企业投资，G 为政府支出，X 为出口，M 为进口。收入法将所有要素收入（工资、租金、利息、利润）加总，而产出法则将各行业的增加值累计。
10. Inflation Rate Calculation | 通货膨胀率计算
The inflation rate shows the percentage increase in the general price level over a period, commonly measured by the Consumer Price Index (CPI). It is a key indicator of economic stability.
通货膨胀率显示一段时期内总体物价水平上升的百分比，通常以消费者物价指数（CPI）衡量。它是经济稳定的关键指标。
Inflation Rate = (CPI current − CPI previous) ÷ CPI previous × 100
A positive rate signals rising prices, reducing the purchasing power of money. Deflation occurs when the rate is negative. Governments and central banks monitor this closely to adjust monetary policy.
通胀率为正表明物价上涨，货币购买力下降。当通胀率为负时，即发生通货紧缩。政府和央行密切监测通胀率以调整货币政策。
11. Unemployment Rate | 失业率
The unemployment rate captures the share of the labour force that is actively seeking work but unable to find a job. It is a vital measure of labour market health.
失业率反映劳动力人口中正在积极寻找工作但无法找到工作的人所占的比重。它是衡量劳动力市场健康状况的重要指标。
Unemployment Rate = (Number of unemployed ÷ Labour force) × 100
The labour force includes those employed plus those unemployed and actively seeking work. Students, retirees, and discouraged workers who have stopped looking are not counted in the labour force, which can affect the official rate.
劳动力人口包括就业者和正在积极寻找工作的失业者。学生、退休人员以及已停止求职的丧失信心的劳动者不计入劳动力人口，这可能影响官方失业率。
12. Exchange Rates and Trade Balance | 汇率与贸易差额
An exchange rate expresses the price of one currency in terms of another. Changes in exchange rates directly influence a country's trade balance by affecting export and import prices.
汇率是用一种货币表示的另一种货币的价格。汇率变动通过影响出口和进口价格，直接影响一国的贸易差额。
%Δ Exchange Rate = (New rate − Old rate) ÷ Old rate × 100
Trade Balance = Value of exports − Value of imports
A currency appreciation (increase in value) makes exports dearer and imports cheaper, potentially worsening the trade balance. A depreciation has the opposite effect. The sum of the current account, capital account and financial account plus net errors and omissions must be zero in the balance of payments.
货币升值（价值上升）使出口变贵、进口变便宜，可能恶化贸易差额。货币贬值则产生相反效果。国际收支中经常账户、资本账户与金融账户之和加上净误差与遗漏必须为零。
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